Inversion Center Research Articles

ISODISTROTLaMTeO6 (M = Ga3+ and Mn3+): the critical role of electronic configuration and cation ordering in crystal structures.

In this work, PbSb2O6-type oxides LaMTeO6 (M = Ga3+ and Mn3+) were synthesized and structurally characterized by Rietveld refinements against high-resolution X-ray powder diffraction data. The Ga3+/Te6+ partial ordering within the honeycomb-like two-dimensional [GaTeO6]3- anionic layer leads to the loss of the inversion center between Ga3+ and Te6+; however the inversion center on the 3̄-roto-inversion axis is preserved, thereby resulting in a 2-fold PbSb2O6-type superstructure by doubling the c-axis associated with a structural symmetry descending from the original P3̄1m to P3̄1c symmetry. In contrast, LaMnTeO6 (P21/c) adopts a monoclinically distorted 4-fold superstructure with lattice dimensions of a ≈ aH, b ≈ √3aH, c ≈ 2cH, where aH and cH represent the lattice parameters of trigonal PbSb2O6. The formation of this P21/c-superstructure is attributed to the combination of complete Mn3+/Te6+ ordering and the first-order Jahn-Teller distortion of Mn3+ with the electronic configuration of d4. Such a monoclinic distortion can effectively lift the Mn3+ spin moments arranged on the triangular sublattice, resulting in a sharp peak for antiferromagnetic transition, which is in stark contrast to subtle magnetic transitions for PbSb2O6-type tellurates AMn(VI)TeO6 (A = alkaline earth and Pb2+) and LnCrTeO6 (Ln = rare earth) with higher structural symmetry. Our findings highlight that the electronic configuration effects of M-cations play a critical role in controlling the structure symmetry of LaMTeO6, providing a strategy to fine-tune the crystal structures and physical properties.

Optical bistability in topological layered structure and its application in photonic neural network

Optical bistable state exhibits its great potential applications in photonic integrated circuit and photonic neural network. However, the traditional optical bistable state will be influenced by the system disorders, which are not suitable for application. In this work, we investigate the topological bistable states in a layered structure with center inversion symmetry consisting of alternating layers of high index material TiO<sub>2</sub> and low index material SiO<sub>2</sub>. In the topological mode, the electric field is highly localized in the inversion center of the layered structure (also known as the interface) and exponentially decays into the bulk. Thus, when the nonlinear permittivity is strategically introduced into those layers, nonlinear phenomena such as the bistable state appears. The finite element numerical simulations reveal that the optimal bistable state appears when the layer period is 5 with a threshold power around 1.2 W/m. Benefiting from the topological characteristics, such a bistable state persists when random perturbations are introduced into the layer thickness and refractive index. Finally, we apply the bistable states to a photonic neural network. The bistable function shows prediction accuracy similar to the classic activation function ReLu and sigmoid in various learning tasks. These results provide a novel method for inserting highly robust optical bistable states from topological layered structure into photonic neural network.

ON THE MAXIMUM CIRCULAR INVERSES OF MAXIMUM CIRCLES

In this study, the inverses of maximum circles under the maximum circular inversion are examined. The maximum circular inversion is observed to transform maximum circles to curves consisting of parabolic arcs, line segments, and sometimes rays. It is seen that the image curve occurs in different shapes depending on the relative positions of the inversion circle and the maximum circle. While the images of maximum circles not passing through the inversion center are closed curves, the images of those passing through the inversion center are not closed. Inverse curves have been studied by considering the radii of the maximum circles and the positions of the lines joining their centers and the center of maximum inversion. Classifications of the inverses of maximum circles are presented.

Bis[1,3-bis-(2,4,6-tri-methyl-phen-yl)imidazolium] bis(μ-cis-1,2-di-phenyl-ethene-1,2-di-thiol-ato-κ2S,S':κS)bis-[(cis-1,2-di-phenyl-ethene-1,2-di-thiol-ato-κ2S,S')iron(III)] di-methyl-formamide disolvate.

The mol-ecular structure of the solvated title salt, (C21H25N2)2[Fe2(C14H10S2)4]·2C3H7NO reveals that the anion is situated on a crystallographic inversion center in the triclinic space group P . The title compound crystallizes utilizing a network of weak π-stacking inter-actions of phenyl rings pertaining to the di-thiol-ene unit. Moreover, the acidic imidazolium H atoms [N-C(H)-N] display non-classical hydrogen-bonding inter-actions of the C-H⋯O type to the oxygen atoms of the N,N-dimethyl formamide solvent, and hydrogen atoms on the backbone of imidazolium rings display weak C-H⋯S inter-actions with the di-thiol-ene sulfur atoms.

Electric Tuning of Vortex Ratchet Effect in NbSe2.

Inversion symmetry breaking has played an important role in recent discoveries of nonreciprocal charge transport. Niobium diselenide, for example, lacks an inversion center in the monolayer form and can host prominent nonreciprocal transport property. Here, however, we observe a nonreciprocal transport signal in the second-harmonic channel of bulk-like NbSe2, in which inversion symmetry of the lattice seems preserved. The second-harmonic signal occurs along different in-plane current orientations and appears not only in the vortex-liquid regime but also even in the superconducting fluctuation regime without an applied magnetic field. By adding a direct current (DC) bias, we quantify the symmetry breaking effect in the vortex-liquid regime. The DC bias also suggests that the rectification effect at the contacts may account for the seemingly nonreciprocal transport at zero magnetic field. Our results demonstrate that DC biasing is a useful knob for addressing nonreciprocal charge transport in a wide range of materials.

Enantiomorph conversion in single crystals of the Weyl semimetal CoSi

Chiral intermetallic phases may show unusual chemical and physical properties with nontrivial structure-property relationship. It is therefore of particular interest to study the structural conversion between domains of different handedness. Here, the atomic decoration of the enantiomorph exchange area within single crystal of the Weyl semimetal CoSi is determined by a combination of atomic-resolution scanning transmission electron microscopy imaging, single crystal X-ray diffraction and quantum chemical analysis of atomic interactions. Two-atomic [CoSi] units are shown to be the bonding base for the FeSi-type structure and may be considered as ‘pseudo-molecules’, thinking of molecular organic crystals. Tiny reorganisation of atomic interactions within these units results in the appearance of sequence ‘faults’ in the structure pattern i.e. in a different structural motif in the enantiomorph exchange area, which – contrary to the A and B enantiomorphs of CoSi – contains an inversion centre and allows a local enantiomorph ‘conversion’. Due to the special features of atomic interactions, the reorganisation of multi-atomic bonds leads to slightly higher total energy. This appears within one and the same grain which is prepared by the short distance chemical vapor transport.

Nonlinear and Emissive {[MIII(CN)6]3-···Polyresorcinol} (M = Fe, Co, Cr) Cocrystals Exhibiting an Ultralow Frequency Raman Response.

Optically active functional noncentrosymmetric architectures might be achieved through the combination of molecules with inscribed optical responses and species of dedicated tectonic character. Herein, we present the new series of noncentrosymmetric cocrystal salt solvates (PPh4)3[M(CN)6](L)n·msolv (M = Cr(III), Fe(III), Co(III); L = polyresorcinol coformers, multiple hydrogen bond donors: 3,3',5,5'-tetrahydroxy-1,19-biphenyl, DiR, n = 2, or 5'-(3,5-dihydroxyphenyl)-3,3″,5,5″-tetrahydroxy-1,19:3',1″-terphenyl, TriRB, n = 1) denoted as MDiR and MTriRB, respectively. The hydrogen-bonded subnetworks {[M(CN)6]3-;Ln}∞ of dmp, neb, or dia topology are formed through structural matching between building blocks within supramolecular cis-bis(chelate)-like {[M(CN)6]3-;(H2L)2(HL)2} or tris(chelate)-like {[M(CN)6]3-;(H2L)3} fragments. The quantum-chemical analysis demonstrates the mixed electrostatic and covalent character of these interactions, with their strength clearly enhanced due to the negative charge of the hydrogen bond acceptor metal complex. The corresponding interaction energy is also dependent on the geometry of the contact and size matching of its components, rotational degree of freedom and extent of the π-electron system of the coformer, and overall fit to the molecular surroundings. Symmetry of the crystal lattices is correlated with the local symmetry of coformers and {complex;(coformer)n} hydrogen-bonded motifs characterized by the absence of the inversion center and mirror plane. All compounds reveal second-harmonic generation activity and photoluminescence diversified by individual UV-vis spectral characteristics of the components, and interesting low-frequency Raman scattering spectra within the subterahertz spectroscopic domain. Vibrational (infrared/Raman), UV-vis electronic absorption (experimental and calculated), and 57Fe Mössbauer spectra together with electrospray ionization mass spectrometry (ESI-MS) data are provided for the complete description of our systems.

A significantly enhanced magnetic moment due to an electric dipole moment

We demonstrate via first-principle calculations based on the density functional theory that the magnetic moment of a helium atom under a given magnetic field has a positive correlation with the electric dipole moment when an external electric field is applied to the system. Our calculation shows that the enhancement of the magnetic moment is significant due to the reduction of the triplet-singlet splitting. We argue that this finding can be generalized to organic molecules, especially to macromolecules where the structure induced an electric dipole moment which may give rise to significantly enhanced responses to the external magnetic field. These results suggest that considerable magnetic responses prevail, particularly in bio-molecules without an inversion center.

Ladder-like Organostannoxane: Synthesis and Crystal Structure of the Second Polymorph {[(C6H5)2Sn]2[(C6H5)2ClSn]2(μ3-O)2(μ2-OH)2}∙[DMF

A ladder-like organostannoxane identified as a polymorph of bis-[chloro-(m2-hydroxo)-(m3-oxo)-tetraphenyl-di-tin] dimethylformamide solvate, {[(C6H5)2Sn]2[(C6H5)2ClSn]2(μ3-O)2(μ2-OH)2}[DMF]2 (1), has been synthesized and structurally characterized by means of single-crystal X-ray diffraction analysis. Compound 1 crystallizes in the monoclinic space group P21/c with a = 23.4137(12) Å, b = 11.2525(6) Å, c = 20.2719(11) Å, β = 100.461(2)°, V = 5252.1(5) Å3, Z = 4 and Z’ = 1. The XRD discloses that the polymorph reported in this work is the full molecule which does not crystallize about any inversion center. Complex 1 exhibits a tetranuclear organotin(IV) ladder-like structure containing two external chlorides. The tetranuclear structure is comprised of a three-rung-staircase Sn4O4 cluster which consists of a ladder of four Sn2O2 units. The central Sn2O2 core forms dihedral angles of 4.00(7)° and 1.62(8)° with its two fused four-membered rings, describing a slightly bent ladder. This folding is further noticed with the dihedral angle between the two external Sn2O2 cores of 4.65(8)°. In the structure, two types of distorted trigonal bipyramid geometry at tin centers like-arrangement are disclosed. The most Sn–O bridges bond lengths describe a static trans effect affording dissymmetrical bonds. The dimethylformamide solvate molecules form a dihedral angle of 74.5(2)° and are interlinked to the tetranuclear organotin(IV) ladder via O–H···O hydrogen bond patterns. Additional inner C–H···Cl and C–H···O hydrogen bonds as well the C–H···O interactions are present. Moreover, the intermolecular C–H···O hydrogen bonds do not contribute to direct the crystal structure framework; they do not play an important function in forming a supramolecular architecture.

A Note on the Maximum Circle Inverses of Lines in the Maximum Plane

In this study, the images of lines under inversion in maximum circle are analytically examined. It is observed that the image of line not passing through the center of the inversion is not a maximum circle, but the closed curve containing at least one parabola arc. Some properties regarding the images of lines are introduced. Then, the images of line segments are examined according to the positions of their end points . In addition, it is seen that the inversion in maximum circle transforms the pencil of parallel lines (except line passing the center) to the set of the closed curves passing the center of inversion. Also, the images of the concurrent lines under inversion with respect to a maximum circle are considered and the results are presented.

Crystal structures of the isotypic complexes bis-(morpholine)-gold(I) chloride and bis-(morpholine)-gold(I) bromide.

The compounds bis-(morpholine-κN)gold(I) chloride, [Au(C4H9NO)2]Cl, 1, and bis-(morpholine-κN)gold(I) bromide, [Au(C4H9NO)2]Br, 2, crystallize isotypically in space group C2/c with Z = 4. The gold atoms, which are axially positioned at the morpholine rings, lie on inversion centres (so that the N-Au-N coordination is exactly linear) and the halide anions on twofold axes. The residues are connected by a classical hydrogen bond N-H⋯halide and by a short gold⋯halide contact to form a layer structure parallel to the bc plane. The morpholine oxygen atom is not involved in classical hydrogen bonding.

Targeting Oxide Concentration in Tantalum Oxide-Fluoride Anions

The design of both molecular and non-molecular solid materials with specific properties fundamentally relies on the controlled synthesis of crystals with desired functional groups, bonding motifs, polarity, chirality, and more. To this end, fluoride and oxide-fluoride anions have been utilized as basic building units (BBUs) in the synthesis of noncentrosymmetric racemic materials for their ability to create polar axes that facilitate the breaking of an inversion center as demonstrated in a series of compounds with [MF6]2- anions (M = Ti, Zr, Hf). Targeting an analog with a [TaOF5]2- anion, the phase space of (CuO, Ta2O5)/bpy/HF(aq)/H2O (bpy = 2,2′-bipyridine) was investigated and three new compounds with Cu-bpy cations and Ta-fluoride or Ta-oxyfluoride anions were synthesized: [Cu(bpy)2][TaF6], [Cu(bpy)2][Ta2OF10], and [Cu(bpy)F(H2O)2]2[TaF7]∙H2O with the anions [TaF6]-, [Ta2OF10]2-, and [TaF7]2-, respectively. The formation of these anions was found to be a product of both the concentration of hydrofluoric acid in solution and the ratio of metal-oxide starting materials to ligand. This work contributes to the understanding of mixed anion formation in the solid state.

Trans-Bis[bis-(di-phenyl-phosphan-yl)methane-κ2P,P']di-chlorido-ruthenium(II): a triclinic polymorph.

The title compound, [RuCl2(C25H22P2)2] or [RuCl2(dppm)2] (dppm = bis-(di-phenyl-phosphan-yl)methane, C25H22P2) crystallizes as two half-mol-ecules (completed by inversion symmetry) in space group P (Z = 2), with the RuII atoms occupying inversion centers at 0,0,0 and 1/2, 1/2, 1/2, respectively. The bidentate phosphane ligands occupy equatorial positions while the chlorido ligands complete the distorted octa-hedral coordination spheres at axial positions. The bite angles of the phosphane chelates are similar for the two mol-ecules [(P-Ru-P)avg. = 71.1°], while there are significant differences in the twisting of the methyl-ene backbone, with a distance of the methyl-ene C atom from the RuP4 plane of 0.659 (2) and 0.299 (3) Å, respectively, and also for the phenyl substituents for both mol-ecules due to variations in weak C-H⋯Cl inter-actions.

Chiral and Achiral Crystal Structures of Au25 (PET)18 0 Reveal Effects of Ligand Rotational Isomerization on Optoelectronic Properties.

The crystal structures of 4 ligand-rotational isomers of Au25 (PET)18 are presented. Two new ligand-rotational isomers are revealed, and two higher-quality structures (allowing complete solution of the ligand shell) of previously solved Au25 (PET)18 clusters are also presented. One of the structures lacks an inversion center, making it the first chiral Au25 (SR)18 structure solved. These structures combined with previously published Au25 (SR)18 structures enable an analysis of the empirical ligand conformation landscape for Au25 (SR)18 clusters. This analysis shows that the dihedral angles within the PET ligand are restricted to certain observable values, and also that the dihedral angle values are interdependent, in a manner reminiscent of biomolecule dihedral angles such as those in proteins and DNA. The influence of ligand conformational isomerism on optical and electronic properties was calculated, revealing that the ligand conformations affect the nanocluster absorption spectrum, which potentially provides a way to distinguish between isomers at low temperature.

Synthesis, crystal structure and properties of tetra-kis-(pyridine-3-carbo-nitrile)-dithio-cyanatoiron(II) and of diaqua-bis-(pyridine-3-carbo-nitrile)-di-thio-cyanatoiron(II) pyridine-3-carbo-nitrile monosolvate.

The reaction of iron thio-cyanate with 3-cyano-pyridine (C6H4N2) leads to the formation of two compounds with the composition [Fe(NCS)2(C6H4N2)4] (1) and [Fe(NCS)2(C6H4N2)2(H2O)2]·2C6H4N2 (2). The asymmetric unit of 1 consists of one iron cation, two thio-cyanate anions and four 3-cyano-pyridine ligands in general positions. The iron cation is octa-hedrally coordinated by two N-bonded thio-cyanate anions and four 3-cyano-pyridine ligands. The complexes are arranged in columns along the crystallographic c-axis direction and are linked by weak C-H⋯N inter-actions. In 2, the asymmetric unit consists of one iron cation on a center of inversion as well as one thio-cyanate anion, one 3-cyano-pyridine ligand, one water ligand and one 3-cyano-pyridine solvate mol-ecule in general positions. The iron cation is octa-hedrally coordinated by two N-bonded thio-cyanate anions, two cyano-pyridine ligands and two water ligands. O-H⋯N and C-H⋯S hydrogen bonding is observed between the water ligands and the solvent 3-cyano-pyridine mol-ecules. In the crystal structure, alternating layers of the iron complexes and the solvated 3-cyano-pyridine mol-ecules are observed. Powder X-ray (PXRD) investigations reveal that both compounds were obtained as pure phases and from IR spectroscopic measurements conclusions on the coordination mode of the thio-canate anions and the cyano-group were made. Thermogravimetric (TG) and differential thermoanalysis (DTA) of 1 indicate the formation of a compound with the composition {[Fe(NCS)2]3(C6H4N2)4}n that is isotypic to the corresponding Cd compound already reported in the literature. TG/DTA of 2 show several mass losses. The first mass loss corresponds to the removal of the two water ligands leading to the formation of 1, which transforms into {[Fe(NCS)2]3(C6H4N2)4}n, upon further heating.

Crystal structure and Hirshfeld surface analysis of bis(3-aminopyrazole-κN 1)bis(3-aminopyrazole-κN 2)bis(nitrato-κO)copper(II)

In the crystal structure of the title compound, [Cu(NO3)2(C3H5N3)4], the CuII atom is situated on an inversion center (Wyckoff position 2c of space group P21/n) and shows an octahedral [N4O2] coordination environment. The axial positions are occupied by O atoms of nitrate anions, while the equatorial positions are taken up by the N atoms of four 3-aminopyrazole ligands. As a result of the tautomerism of the latter, two coordinate with the N1-atom of 3-aminopyrazole while the other two with the N2-atom. The presence of pyrrole-like N—H groups and amine substituents as donor groups leads to numerous intra- and intermolecular hydrogen-bonding interactions, which were quantified by Hirshfeld surface analysis.

Synthesis, crystal structure and Hirshfeld surface analysis of diaquabis(o-phenylenediamine-κ2 N,N′)nickel(II) naphthalene-1,5-disulfonate

The reaction of o-phenylenediamine (OPD), sodium naphthalene1,5-disulfonate (Na2NDS) and nickel sulfate in an ethanol–water mixture yielded the title compound, [Ni(OPD)2(H2O)2]·NDS or [Ni(C6H8N2)2(H2O)2](C10H6O6S2). This salt consists of a complex [Ni(OPD)2(H2O)2]2+ cation with two bidentate OPD ligands and trans aqua ligands, and a non-coordinating NDS2– anion, which is the double-deprotonated form of H2NDS. The NiII atom is situated at a center of inversion and exhibits a slightly tetragonally distorted {O2N4} octahedral coordination environment, with four shorter equatorial Ni—N bonds [2.0775 (17) and 2.0924 (18) Å] and a longer axial Ni—O bond [2.1381 (17) Å]. The OPD ligand is located about an inversion center and is nearly coplanar with the NiN4 plane [dihedral angle 0.95 (9)°]. In the crystal, the cations and anions are connected by charge-assisted intermolecular N—H...O and O—H...O hydrogen-bonding interactions into the tri-periodic network structure. Hirshfeld surface analysis indicates that the most important contributions to the crystal packing are from H...H (44.1%), O...H/H...O (34.3%), C...H/H...C (14.8%) C...C (6.5%) (involving the cations) and O...H/H...O (50%), H...H (25%), C...H/H...C (15.3%), C...C (8.2%) (involving the anions) interactions.

Bis(diisobutylammonium) tetrachloridobis[3-(trifluoromethyl)phenyl]stannate

The asymmetric unit in the title salt, (C8H20N)2[SnCl4(C7H4Cl2F3)2], features a di-isobutylammonium cation in a general position and a diorganotin tetrachloride dianion, i.e. tetrachloridobis(3-trifuoromethylphenyl)stannate(IV), located on a centre of inversion; the SnIV atom is octahedrally coordinated. In the crystal, charge-assisted N+—H...Cl hydrogen bonds along with C—H...F contacts occur within supramolecular layers that interdigitate along the a-axis direction.

Synthesis, crystal structure and thermal properties of poly[[μ-1,2-bis-(pyridin-4-yl)ethene-κ2N:N'-μ-bromido-copper(I)] 1,2-bis-(pyridin-4-yl)ethene 0.25-solvate

The reaction of copper(I) bromide with 1,2-bis-(pyridin-4-yl)ethene in aceto-nitrile leads to the formation of the title compound, {[CuBr(C12H10N2)]·0.25C12H10N2}n or CuBr(4-bpe)·0.25(4-bpe) [4-bpe = 1,2-bis-(pyridin-4-yl)ethene]. The asymmetric unit consists of one copper(I) cation and one bromide anion in general positions as well as two crystallographically independent half 4-bpe ligands and a quarter of a disordered 4-bpe solvate mol-ecule that are completed by centers of inversion. The copper(I) cations are tetra-hededrally coordinated as CuBr2N2 and linked by pairs of μ-1,1-bridging bromide anions into centrosymmetric dinuclear units that are further connected into layers by the 4-bpe coligands. Between the layers, inter-layer C-H⋯Br hydrogen bonding is observed. The layers are arranged in such a way that cavities are formed in which the disordered 4-bpe solvate mol-ecules are located. Powder X-ray (PXRD) investigations reveal that a pure sample has been obtained. Thermogravimetric (TG) and differential thermoanalysis (DTA) measurements show two mass losses that are accompanied by endothermic events in the DTA curve. The first mass loss correspond to the removal of 0.75 4-bpe mol-ecules, leading to the formation of (CuBr)2(4-bpe), already reported in the literature as proven by PXRD.

Synthesis, crystal structure and Hirshfeld surface analysis of di-acetato-bis-[4-(2-amino-eth-yl)morpholine]cadmium tetra-hydrate.

The title coordination compound, [Cd(C2H3O2)2(C6H14N2O)2]·4H2O, was synthesized by mixing 2 moles of 4-(2-amino-eth-yl)morpholine and 1 mole of cadmium acetate in double-distilled water. The Cd atom is octa-hedrally coord-inated by two N,N'-bidentate ligands [4-(2-amino-eth-yl)morpholine] and two trans-located acetate mol-ecules. The Cd atom is located on a center of inversion, whereas the 4-(2-amino-eth-yl)morpholine and four water mol-ecules are adjacent to the acetate mol-ecules. The chair conformation of the morpholine mol-ecules is confirmed. In the crystal, adjacent metal complexes and uncoord-inated water mol-ecules are linked via N-H⋯O and O-H⋯O hydrogen-bonding inter-actions, generating R 2 2(6), R 6 6(16), R 6 6(20) and S 1 1(6) motifs and forming a three-dimensional network. A Hirshfeld surface analysis indicated the contributions of various contacts: H⋯H (71.8%), O⋯H/H⋯O (27.1%), and C⋯H/H⋯C (1.0%).